Chromaticity of a family of 5-partite graphs

AbstractLet P(G,λ) be the chromatic polynomial of a graph G. Two graphs G and H are said to be chromatically equivalent, denoted G∼H, if P(G,λ)=P(H,λ). We write [G]={H∣H∼G}. If [G]={G}, then G is said to be chromatically unique. In this paper, we first characterize certain complete 5-partite graphs G with 5n vertices according to the number of 6-independent partitions of G. Using these results, we investigate the chromaticity of G with certain stars or matching deleted parts . As a by-product, two new families of chromatically unique complete 5-partite graphs G with certain stars or matching deleted parts are obtained

Chemical Instability of the Cobalt Oxyhydrate Superconductor under Ambient Conditions

The layered sodium cobalt oxyhydrate superconductor Na0.3CoO2*1.4H2O is shown through X-ray diffraction and thermogravimetric studies to be one of a series of hydrated phases of Na0.3CoO2. Further, it is shown that the material is exceptionally sensitive to both temperature and humidity near ambient conditions, easily dehydrating to a non-superconducting lower hydrate. The observation of this stable lower hydrate with c=13.8 angstroms implies that the superconductivity turns on in this system between CoO2 layer spacings of 6.9 and 9.9 angstroms at nominally constant chemical doping.Comment: 10 pages and 4 figure

Stuffed Rare Earth Pyrochlore Solid Solutions

Synthesis and crystal structures are described for the compounds Ln2(Ti2-xLnx)O7-x/2, where Ln = Tb, Dy, Ho, Er, Tm, Yb, Lu, and x ranges from 0 to 0.67. Rietveld refinements on X-ray powder diffraction data indicate that in Tb and Dy titanate pyrochlores, extra Ln3+ cations mix mainly on the Ti4+ site with little disorder on the original Ln3+ site. For the smaller rare earths (Ho-Lu), stuffing additional lanthanide ions results in a pyrochlore to defect fluorite transition, where the Ln3+ and Ti4+ ions become completely randomized at the maximum (x=0.67). In all of these Ln-Ti-O pyrochlores, the addition of magnetic Ln3+ in place of nonmagnetic Ti4+ adds edge sharing tetrahedral spin interactions to a normally corner sharing tetrahedral network of spins. The increase in spin connectivity in this family of solid solutions represents a new avenue for investigating geometrical magnetic frustration in the rare earth titanate pyrochlores.Comment: 25 pages, 7 figures, submitted to J. Solid State Che

Modeling phase behavior for quantifying micro-pervaporation experiments

We present a theoretical model for the evolution of mixture concentrations in a micro-pervaporation device, similar to those recently presented experimentally. The described device makes use of the pervaporation of water through a thin PDMS membrane to build up a solute concentration profile inside a long microfluidic channel. We simplify the evolution of this profile in binary mixtures to a one-dimensional model which comprises two concentration-dependent coefficients. The model then provides a link between directly accessible experimental observations, such as the widths of dense phases or their growth velocity, and the underlying chemical potentials and phenomenological coefficients. It shall thus be useful for quantifying the thermodynamic and dynamic properties of dilute and dense binary mixtures.Comment: to be published in EPJ-

Lattice distortions in a sawtooth chain with Heisenberg and Ising bonds

An exactly solvable model of the sawtooth chain with Ising and Heisenberg bonds and with coupling to lattice distortion for Heisenberg bonds is considered in the magnetic field. Using the direct transfer-matrix formalism an exact description of the thermodynamic functions is obtained. The ground state phase diagrams for all regions of parameters values containing phases corresponding to the magnetization plateaus at $M=0,1/4$ and 1/2 have been obtained. Exact formulas for bond distortions for various ground states are presented. A novel mechanism of magnetization plateau stabilization corresponding to $M=1/4$ state is reported.Comment: 16 pages, 12 figure

Interchange Slip-Running Reconnection and Sweeping SEP Beams

We present a new model to explain how particles (solar energetic particles; SEPs), accelerated at a reconnection site that is not magnetically connected to the Earth, could eventually propagate along the well-connected open flux tube. Our model is based on the results of a low-beta resistive magnetohydrodynamics simulation of a three-dimensional line-tied and initially current-free bipole, that is embedded in a non-uniform open potential field. The topology of this configuration is that of an asymmetric coronal null-point, with a closed fan surface and an open outer spine. When driven by slow photospheric shearing motions, field lines, initially fully anchored below the fan dome, reconnect at the null point, and jump to the open magnetic domain. This is the standard interchange mode as sketched and calculated in 2D. The key result in 3D is that, reconnected open field lines located in the vicinity of the outer spine, keep reconnecting continuously, across an open quasi-separatrix layer, as previously identified for non-open-null-point reconnection. The apparent slipping motion of these field lines leads to form an extended narrow magnetic flux tube at high altitude. Because of the slip-running reconnection, we conjecture that if energetic particles would be traveling through, or be accelerated inside, the diffusion region, they would be successively injected along continuously reconnecting field lines that are connected farther and farther from the spine. At the scale of the full Sun, owing to the super-radial expansion of field lines below 3 solar radii, such energetic particles could easily be injected in field lines slipping over significant distances, and could eventually reach the distant flux tube that is well-connected to the Earth

2022 Upgrade and Improved Low Frequency Camera Sensitivity for CMB Observation at the South Pole

Constraining the Galactic foregrounds with multi-frequency Cosmic Microwave Background (CMB) observations is an essential step towards ultimately reaching the sensitivity to measure primordial gravitational waves (PGWs), the sign of inflation after the Big-Bang that would be imprinted on the CMB. The BICEP Array telescope is a set of multi-frequency cameras designed to constrain the energy scale of inflation through CMB B-mode searches while also controlling the polarized galactic foregrounds. The lowest frequency BICEP Array receiver (BA1) has been observing from the South Pole since 2020 and provides 30 GHz and 40 GHz data to characterize the Galactic synchrotron in our CMB maps. In this paper, we present the design of the BA1 detectors and the full optical characterization of the camera including the on-sky performance at the South Pole. The paper also introduces the design challenges during the first observing season including the effect of out-of-band photons on detectors performance. It also describes the tests done to diagnose that effect and the new upgrade to minimize these photons, as well as installing more dichroic detectors during the 2022 deployment season to improve the BA1 sensitivity. We finally report background noise measurements of the detectors with the goal of having photon noise dominated detectors in both optical channels. BA1 achieves an improvement in mapping speed compared to the previous deployment season.Comment: Proceedings of SPIE Astronomical Telescopes + Instrumentation 2022 (AS22

Manufacturing flow line systems: a review of models and analytical results

The most important models and results of the manufacturing flow line literature are described. These include the major classes of models (asynchronous, synchronous, and continuous); the major features (blocking, processing times, failures and repairs); the major properties (conservation of flow, flow rate-idle time, reversibility, and others); and the relationships among different models. Exact and approximate methods for obtaining quantitative measures of performance are also reviewed. The exact methods are appropriate for small systems. The approximate methods, which are the only means available for large systems, are generally based on decomposition, and make use of the exact methods for small systems. Extensions are briefly discussed. Directions for future research are suggested.National Science Foundation (U.S.) (Grant DDM-8914277